What is the derivative of ((x+1/(x-1))^2) ?

The derivative of ((x+1/(x-1))^2) is -(4(x+1))/((x-1)^3)

What is the first derivative of ((x+1/(x-1))^2) ?

The first derivative of ((x+1/(x-1))^2) is -(4(x+1))/((x-1)^3)

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\frac{d}{d x} ((\frac{x + 1}{x - 1})^{2})

- \frac{4 ( x + 1 )}{( x - 1 ) ^{3}}

Solution steps

\frac{d}{d x} ((\frac{x + 1}{x - 1})^{2})

Apply the chain rule:

2 \cdot \frac{x + 1}{x - 1} \frac{d}{d x} (\frac{x + 1}{x - 1})

= 2 \cdot \frac{x + 1}{x - 1} \frac{d}{d x} (\frac{x + 1}{x - 1})

\frac{d}{d x} (\frac{x + 1}{x - 1}) = - \frac{2}{( x - 1 ) ^{2}}

= 2 \cdot \frac{x + 1}{x - 1} (- \frac{2}{( x - 1 ) ^{2}})

Simplify

2 \cdot \frac{x + 1}{x - 1} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{4 ( x + 1 )}{( x - 1 ) ^{3}}

= - \frac{4 ( x + 1 )}{( x - 1 ) ^{3}}

2 + x

f (t) = 6 t^{3} e^{- 2 t}

x \to 4 lim (\frac{x ^{2} - 9}{x - 3})

\frac{sec ^{2} ( x )}{2}, 2 cos^{2} (x)

x \to 2 lim (4 x^{2} - 11 x - 2)

What is the derivative of ((x+1/(x-1))^2) ?
The derivative of ((x+1/(x-1))^2) is -(4(x+1))/((x-1)^3)
What is the first derivative of ((x+1/(x-1))^2) ?
The first derivative of ((x+1/(x-1))^2) is -(4(x+1))/((x-1)^3)